Understanding the genetic constraints on pathogen evolution will help to predict the emergence of generalist pathogens that can infect a range of different host genotypes. Here we show that generalist viral pathogens are more likely to emerge during coevolution between the bacterium Pseudomonas fluorescens and the lytic phage SBW25Φ2 than when the same pathogen is challenged to adapt to a nonevolving population of novel hosts. When phages were able to adapt to nonevolving novel hosts, the resulting phenotypes had relatively narrow host ranges compared with coevolved phages. Evolved (rather than coevolved) phages also had lower virulence, although they attained virulence similar to that of coevolved phages after continued adaptation to a nonevolving population of the same host. We explain these results by using sequence data showing that the evolution of broad host range is associated with several different amino acid substitutions and therefore occurs only through repeated rounds of selection for novel infectivity alleles. These findings suggest that generalist bacteriophages are more likely to emerge through long-term coevolution with their hosts than through spontaneous adaptation to a single novel host. These results are likely to be relevant to host-parasite systems where parasite generalism can evolve through the acquisition of multiple mutations or alleles, as appears to be the case for many plant-bacteria and bacteria-virus interactions.